where Pn2+1⁡(ζ) and Qn2⁡(ζ) are polynomials of degrees
n2+1 and n2, respectively, with no common zeros. For examples and plots
see Clarkson (2003a) and Milne et al. (1997). Similar results hold
when δ=0 and β⁢γ≠0.

with C an arbitrary constant, which is solvable by quadrature. For examples
and plots see Clarkson (2005). PV, with α=β=0 and
γ2+2⁢δ=0, has solutions w⁡(z)=C⁢exp⁡(±-2⁢δ⁢z),
with C an arbitrary constant.